Average Error: 0.0 → 0.5
Time: 11.9s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left({c}^{5}, \frac{1}{120}, c\right)\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left({c}^{5}, \frac{1}{120}, c\right)\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r9687 = c;
        double r9688 = sinh(r9687);
        double r9689 = -2.9807307601812193e+165;
        double r9690 = 2.0;
        double r9691 = pow(r9689, r9690);
        double r9692 = r9687 - r9691;
        double r9693 = fmod(r9688, r9692);
        return r9693;
}
↓
double f(double c) {
        double r9694 = 0.16666666666666666;
        double r9695 = c;
        double r9696 = 3.0;
        double r9697 = pow(r9695, r9696);
        double r9698 = 5.0;
        double r9699 = pow(r9695, r9698);
        double r9700 = 0.008333333333333333;
        double r9701 = fma(r9699, r9700, r9695);
        double r9702 = fma(r9694, r9697, r9701);
        double r9703 = -2.9807307601812193e+165;
        double r9704 = 2.0;
        double r9705 = pow(r9703, r9704);
        double r9706 = r9695 - r9705;
        double r9707 = fmod(r9702, r9706);
        return r9707;
}

Error

Bits error versus c

Derivation

  1. Initial program 0.0

    \[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]

  2. Taylor expanded around 0 0.5

    \[\leadsto \left(\color{blue}{\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right)} \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]

  3. Simplified0.5

    \[\leadsto \left(\color{blue}{\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left({c}^{5}, \frac{1}{120}, c\right)\right)\right)} \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]

  4. Final simplification0.5

    \[\leadsto \left(\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left({c}^{5}, \frac{1}{120}, c\right)\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 014"
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2.0))))